HTTP adaptive streaming is being increasingly deployed by network content providers, such as Netflix and YouTube. By dividing video content into data chunks encoded at different bitrates, a client is able to request the appropriate bitrate for the segment to be played next based on the estimated network conditions. However, this can introduce a number of impairments, including compression artifacts and rebuffering events, which can severely impact an end-user's quality of experience (QoE). We have recently created a new video quality database, which simulates a typical video streaming application, using long video sequences and interesting Netflix content. Going beyond previous efforts, the new database contains highly diverse and contemporary content, and it includes the subjective opinions of a sizable number of human subjects regarding the effects on QoE of both rebuffering and compression distortions. We observed that rebuffering is always obvious and unpleasant to subjects, while bitrate changes may be less obvious due to content-related dependencies. Transient bitrate drops were preferable over rebuffering only on low complexity video content, while consistently low bitrates were poorly tolerated. We evaluated different objective video quality assessment algorithms on our database and found that objective video quality models are unreliable for QoE prediction on videos suffering from both rebuffering events and bitrate changes. This implies the need for more general QoE models that take into account objective quality models, rebuffering-aware information, and memory. The publicly available video content as well as metadata for all of the videos in the new database can be found at http://live.ece.utexas.edu/research/LIVE_NFLXStudy/nflx_index.html.